FDM solutions to linear dynamics of porous media: Efficiency, stability, and parallel solution strategy

Summary This paper presents a strategy to improve the efficiency of simulations involving porous materials with linear behaviour and full saturation. The method is named parallel‐lines finite difference and uses a method to decouple a discretised version of the governing equations allowing parallel...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2017-12, Vol.112 (11), p.1539-1563
Main Authors: Zhang, Yunpeng, Pedroso, Dorival M., Li, Ling, Ehlers, Wolfgang
Format: Article
Language:English
Subjects:
Computer simulation
Dynamic stability
dynamical systems
Efficiency
Finite difference method
finite difference methods
Formulations
implicit
multifield systems
parallelization
Porous materials
Porous media
stability
time integration
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Summary:Summary This paper presents a strategy to improve the efficiency of simulations involving porous materials with linear behaviour and full saturation. The method is named parallel‐lines finite difference and uses a method to decouple a discretised version of the governing equations allowing parallel computations. As a result, the complexity and the bandwidth of the global matrix are significantly reduced and hence the efficiency is improved. The other advantage of the scheme is the fulfilment of the inf‐sup stability condition. The scheme is developed to solve porous media formulations derived from the theory of porous media. Both the u‐p and u‐v‐p formulations are considered (u: displacement of solid, p: pressure of liquid, and v: velocity of liquid). Several simulations are performed to demonstrate the capabilities of the method.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.5568